{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Method development for geometric functions pt 2: $\\beta$ parameters with geometric functions.\n", "\n", "- 09/04/20 debugged\n", "- 26/02/20 v1\n", "\n", "Aims:\n", "\n", "- Develop $\\beta_{L,M}$ formalism.\n", "- Develop corresponding numerical methods - see [pt 1 notebook](https://epsproc.readthedocs.io/en/dev/methods/geometric_method_dev_260220_tidy_160320.html).\n", "- Analyse geometric terms - see [pt 1 notebook](https://epsproc.readthedocs.io/en/dev/methods/geometric_method_dev_260220_tidy_160320.html)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\beta_{L,M}^{MF}$ rewrite\n", "\n", "The various terms defined above can be used to redefine the full MF observables, expressed as a set of $\\beta_{L,M}$ coefficients." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The original (full) form for the MF equation, as implemented in `ePSproc.mfblm()` (note this is defined for an expansion in non-conjugate harmonics, $Y_{LM}(\\theta_{\\hat{k}},\\phi_{\\hat{k}})$):\n", "\n", "\\begin{eqnarray}\n", "\\beta_{L,-M}^{\\mu_{i},\\mu_{f}} & = & \\sum_{l,m,\\mu}\\sum_{l',m',\\mu'}(-1)^{M}(-1)^{m}(-1)^{(\\mu'-\\mu_{0})}\\left(\\frac{(2l+1)(2l'+1)(2L+1)}{4\\pi}\\right)^{1/2}\\left(\\begin{array}{ccc}\n", "l & l' & L\\\\\n", "0 & 0 & 0\n", "\\end{array}\\right)\\left(\\begin{array}{ccc}\n", "l & l' & L\\\\\n", "-m & m' & -M\n", "\\end{array}\\right)\\nonumber \\\\\n", " & \\times & \\sum_{P,R',R}(2P+1)(-1)^{(R'-R)}\\left(\\begin{array}{ccc}\n", "1 & 1 & P\\\\\n", "\\mu & -\\mu' & R'\n", "\\end{array}\\right)\\left(\\begin{array}{ccc}\n", "1 & 1 & P\\\\\n", "\\mu_{0} & -\\mu_{0} & R\n", "\\end{array}\\right)D_{-R',-R}^{P}(R_{\\hat{n}})I_{l,m,\\mu}^{p_{i}\\mu_{i},p_{f}\\mu_{f}}(E)I_{l',m',\\mu'}^{p_{i}\\mu_{i},p_{f}\\mu_{f}*}(E)\n", "\\end{eqnarray}\n", "\n", "Where $I_{l,m,\\mu}^{p_{i}\\mu_{i},p_{f}\\mu_{f}}(E)$ are the energy-dependent dipole matrix elements." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Substituting the terms above (plus some tidying up with phases etc. - see other notes for full derivation):\n", "\n", "\\begin{eqnarray}\n", "\\beta_{L,-M}^{\\mu_{i},\\mu_{f}} & = & \\sum_{l,m,\\mu}\\sum_{l',m',\\mu'}(-1)^{(\\mu'-\\mu_{0})}{B_{L,-M}}\\nonumber \\\\\n", " & \\times & \\sum_{P,R',R}(2P+1)^{\\frac{1}{2}}{E_{P-R}(\\hat{e})\\Lambda_{R',R}(R_{\\hat{n}})}I_{l,m,\\mu}^{p_{i}\\mu_{i},p_{f}\\mu_{f}}(E)I_{l',m',\\mu'}^{p_{i}\\mu_{i},p_{f}\\mu_{f}*}(E)\n", "\\end{eqnarray}\n", "\n", "And can also reorder...\n", "\n", "\\begin{eqnarray*}\n", "\\beta_{L,-M}^{\\mu_{i},\\mu_{f}} & = & \\sum_{P,R',R}(2P+1)^{\\frac{1}{2}}{E_{P-R}(\\hat{e})}\\sum_{l,m,\\mu}\\sum_{l',m',\\mu'}(-1)^{(\\mu'-\\mu_{0})}{B_{L,-M}\\Lambda_{R',R}(R_{\\hat{n}})}I_{l,m,\\mu}^{p_{i}\\mu_{i},p_{f}\\mu_{f}}(E)I_{l',m',\\mu'}^{p_{i}\\mu_{i},p_{f}\\mu_{f}*}(E)\n", "\\end{eqnarray*}\n", "\n", "Add additional (function) labels to track QNs:\n", "\n", "\\begin{eqnarray*}\n", "\\beta_{L,-M}^{\\mu_{i},\\mu_{f}} & = & \\sum_{P,R',R}(2P+1)^{\\frac{1}{2}}{E_{P-R}(\\hat{e};\\mu_{0})}\\sum_{l,m,\\mu}\\sum_{l',m',\\mu'}(-1)^{(\\mu'-\\mu_{0})}{\\Lambda_{R',R}(R_{\\hat{n}};\\mu,P,R,R')B_{L,-M}(l,l',m,m')}I_{l,m,\\mu}^{p_{i}\\mu_{i},p_{f}\\mu_{f}}(E)I_{l',m',\\mu'}^{p_{i}\\mu_{i},p_{f}\\mu_{f}*}(E)\n", "\\end{eqnarray*}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cf. R\\&U rotational wavepacket case, see also Chpt. 12 in Quantum\n", "Met book for similar formalism separating geometric channels:\n", "\n", "\\begin{equation}\n", "\\varUpsilon_{L,M}^{u}=\\sum_{ll'}\\sum_{\\lambda\\lambda'}\\sum_{mm'}(-1)^{m}\\sqrt{\\frac{(2l+1)(2l'+1)(2L+1)}{4\\pi}}\\left(\\begin{array}{ccc}\n", "l & l' & L\\\\\n", "m & -m' & M\n", "\\end{array}\\right)\\left(\\begin{array}{ccc}\n", "l & l' & L\\\\\n", "0 & 0 & 0\n", "\\end{array}\\right)\\gamma_{\\alpha_{+}l\\lambda ml'\\lambda'm'}^{u}\\label{eq:geom-channels}\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", "\\Lambda^{\\zeta\\zeta'}=\\sum_{\\Gamma,\\Gamma'}\\sum_{\\mu,\\mu'}\\sum_{h,h'}b_{hl\\lambda}^{\\Gamma\\mu*}b_{h'l'\\lambda'}^{\\Gamma'\\mu'}\\boldsymbol{D}_{hl}^{\\Gamma\\mu*}(q,\\,k)\\boldsymbol{D}_{h'l'}^{\\Gamma'\\mu'}(q',\\,k)\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", "\\beta_{L,M}^{u}=\\sum_{\\zeta,\\zeta'}\\varUpsilon_{L,M}^{u,\\zeta\\zeta'}\\Lambda^{\\zeta\\zeta'}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For details on each term in the tensor product, see the [pt 1 notebook](https://epsproc.readthedocs.io/en/dev/methods/geometric_method_dev_260220_tidy_160320.html). Here we'll look at the overall result, check for consistency and benchmark." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* pyevtk not found, VTK export not available. \n" ] } ], "source": [ "# Imports\n", "import numpy as np\n", "import pandas as pd\n", "import xarray as xr\n", "\n", "# Special functions\n", "# from scipy.special import sph_harm\n", "import spherical_functions as sf\n", "import quaternion\n", "\n", "# Performance & benchmarking libraries\n", "# from joblib import Memory\n", "# import xyzpy as xyz\n", "import numba as nb\n", "\n", "# Timings with ttictoc or time\n", "# https://github.com/hector-sab/ttictoc\n", "from ttictoc import TicToc\n", "import time\n", "\n", "# Package fns.\n", "# For module testing, include path to module here\n", "import sys\n", "import os\n", "modPath = r'D:\\code\\github\\ePSproc' # Win test machine\n", "# modPath = r'/home/femtolab/github/ePSproc/' # Linux test machine\n", "sys.path.append(modPath)\n", "import epsproc as ep\n", "# TODO: tidy this up!\n", "# from epsproc.util import matEleSelector\n", "# from epsproc.geomFunc import geomCalc" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "*** ePSproc readMatEle(): scanning files for DumpIdy segments.\n", "\n", "*** Scanning file(s)\n", "['D:\\\\code\\\\github\\\\ePSproc\\\\data\\\\photoionization\\\\n2_3sg_0.1-50.1eV_A2.inp.out']\n", "\n", "*** Reading ePS output file: D:\\code\\github\\ePSproc\\data\\photoionization\\n2_3sg_0.1-50.1eV_A2.inp.out\n", "Expecting 51 energy points.\n", "Expecting 2 symmetries.\n", "Scanning CrossSection segments.\n", "Expecting 102 DumpIdy segments.\n", "Found 102 dumpIdy segments (sets of matrix elements).\n", "\n", "Processing segments to Xarrays...\n", "Processed 102 sets of DumpIdy file segments, (0 blank)\n", "*** ePSproc readMatEle(): scanning files for CrossSection segments.\n", "\n", "*** Scanning file(s)\n", "['D:\\\\code\\\\github\\\\ePSproc\\\\data\\\\photoionization\\\\n2_3sg_0.1-50.1eV_A2.inp.out']\n", "\n", "*** Reading ePS output file: D:\\code\\github\\ePSproc\\data\\photoionization\\n2_3sg_0.1-50.1eV_A2.inp.out\n", "Expecting 51 energy points.\n", "Expecting 2 symmetries.\n", "Scanning CrossSection segments.\n", "Expecting 3 CrossSection segments.\n", "Found 3 CrossSection segments (sets of results).\n", "Processed 3 sets of CrossSection file segments, (0 blank)\n" ] } ], "source": [ "# Load data from modPath\\data\n", "dataPath = os.path.join(modPath, 'data', 'photoionization')\n", "dataFile = os.path.join(dataPath, 'n2_3sg_0.1-50.1eV_A2.inp.out') # Set for sample N2 data for testing\n", "\n", "# Scan data file\n", "dataSet = ep.readMatEle(fileIn = dataFile)\n", "dataXS = ep.readMatEle(fileIn = dataFile, recordType = 'CrossSection') # XS info currently not set in NO2 sample file." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=r, thres=0.01, with Seaborn\n" ] }, { "data": { "text/html": [ "
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| -2 | \n", "SG | \n", "PU | \n", "0.512102-0.000000j | \n", "0.586763+0.000000j | \n", "0.614632-0.000000j | \n", "0.622681-0.000000j | \n", "0.618586-0.000000j | \n", "0.606800-0.000000j | \n", "0.590309-0.000000j | \n", "0.571219+0.000000j | \n", "0.551014+0.000000j | \n", "0.530717-0.000000j | \n", "... | \n", "0.322705+0.000000j | \n", "0.323603+0.000000j | \n", "0.324693-0.000000j | \n", "0.325966-0.000000j | \n", "0.327414+0.000000j | \n", "0.329029+0.000000j | \n", "0.330804+0.000000j | \n", "0.332734+0.000000j | \n", "0.334812+0.000000j | \n", "0.337033+0.000000j | \n", "|||
| 2 | \n", "SG | \n", "PU | \n", "0.512102-0.000000j | \n", "0.586763+0.000000j | \n", "0.614632-0.000000j | \n", "0.622681-0.000000j | \n", "0.618586-0.000000j | \n", "0.606800-0.000000j | \n", "0.590309-0.000000j | \n", "0.571219+0.000000j | \n", "0.551014+0.000000j | \n", "0.530717-0.000000j | \n", "... | \n", "0.322705+0.000000j | \n", "0.323603+0.000000j | \n", "0.324693-0.000000j | \n", "0.325966-0.000000j | \n", "0.327414+0.000000j | \n", "0.329029+0.000000j | \n", "0.330804+0.000000j | \n", "0.332734+0.000000j | \n", "0.334812+0.000000j | \n", "0.337033+0.000000j | \n", "|||
| y | \n", "0 | \n", "SG | \n", "PU | \n", "-0.272711+0.000000j | \n", "-0.638474-0.000000j | \n", "-0.775003-0.000000j | \n", "-0.814436-0.000000j | \n", "-0.794373+0.000000j | \n", "-0.736632-0.000000j | \n", "-0.655845-0.000000j | \n", "-0.562321-0.000000j | \n", "-0.463340-0.000000j | \n", "-0.363902-0.000000j | \n", "... | \n", "0.655141+0.000000j | \n", "0.650741-0.000000j | \n", "0.645402+0.000000j | \n", "0.639166+0.000000j | \n", "0.632075+0.000000j | \n", "0.624163+0.000000j | \n", "0.615465+0.000000j | \n", "0.606012-0.000000j | \n", "0.595832-0.000000j | \n", "0.584952+0.000000j | \n", "||
| -2 | \n", "SG | \n", "PU | \n", "-0.512102+0.000000j | \n", "-0.586763+0.000000j | \n", "-0.614632+0.000000j | \n", "-0.622681+0.000000j | \n", "-0.618586+0.000000j | \n", "-0.606800+0.000000j | \n", "-0.590309+0.000000j | \n", "-0.571219+0.000000j | \n", "-0.551014+0.000000j | \n", "-0.530717+0.000000j | \n", "... | \n", "-0.322705+0.000000j | \n", "-0.323603+0.000000j | \n", "-0.324693+0.000000j | \n", "-0.325966+0.000000j | \n", "-0.327414+0.000000j | \n", "-0.329029+0.000000j | \n", "-0.330804+0.000000j | \n", "-0.332734+0.000000j | \n", "-0.334812+0.000000j | \n", "-0.337033+0.000000j | \n", "|||
| 2 | \n", "SG | \n", "PU | \n", "-0.512102-0.000000j | \n", "-0.586763-0.000000j | \n", "-0.614632-0.000000j | \n", "-0.622681-0.000000j | \n", "-0.618586-0.000000j | \n", "-0.606800-0.000000j | \n", "-0.590309-0.000000j | \n", "-0.571219-0.000000j | \n", "-0.551014-0.000000j | \n", "-0.530717-0.000000j | \n", "... | \n", "-0.322705-0.000000j | \n", "-0.323603-0.000000j | \n", "-0.324693-0.000000j | \n", "-0.325966-0.000000j | \n", "-0.327414-0.000000j | \n", "-0.329029-0.000000j | \n", "-0.330804-0.000000j | \n", "-0.332734-0.000000j | \n", "-0.334812-0.000000j | \n", "-0.337033-0.000000j | \n", "|||
| 4 | \n", "x | \n", "0 | \n", "SG | \n", "PU | \n", "-0.059474-0.000000j | \n", "0.271217+0.000000j | \n", "0.432955-0.000000j | \n", "0.521218-0.000000j | \n", "0.562256-0.000000j | \n", "0.570921-0.000000j | \n", "0.557098-0.000000j | \n", "0.527855+0.000000j | \n", "0.488402+0.000000j | \n", "0.442583-0.000000j | \n", "... | \n", "-0.522724+0.000000j | \n", "-0.532915+0.000000j | \n", "-0.542405+0.000000j | \n", "-0.551224+0.000000j | \n", "-0.559398+0.000000j | \n", "-0.566951-0.000000j | \n", "-0.573903-0.000000j | \n", "-0.580274-0.000000j | \n", "-0.586083+0.000000j | \n", "-0.591343+0.000000j | \n", "|
| -2 | \n", "SG | \n", "PU | \n", "0.080503-0.000000j | \n", "-0.153387-0.000000j | \n", "-0.252803-0.000000j | \n", "-0.294656-0.000000j | \n", "-0.300540-0.000000j | \n", "-0.282866+0.000000j | \n", "-0.249932-0.000000j | \n", "-0.207619-0.000000j | \n", "-0.160148-0.000000j | \n", "-0.110502-0.000000j | \n", "... | \n", "0.555041+0.000000j | \n", "0.556708+0.000000j | \n", "0.557821-0.000000j | \n", "0.558406+0.000000j | \n", "0.558483+0.000000j | \n", "0.558074+0.000000j | \n", "0.557198-0.000000j | \n", "0.555870+0.000000j | \n", "0.554108+0.000000j | \n", "0.551925+0.000000j | \n", "|||
| 2 | \n", "SG | \n", "PU | \n", "0.080503-0.000000j | \n", "-0.153387-0.000000j | \n", "-0.252803-0.000000j | \n", "-0.294656-0.000000j | \n", "-0.300540-0.000000j | \n", "-0.282866+0.000000j | \n", "-0.249932-0.000000j | \n", "-0.207619-0.000000j | \n", "-0.160148-0.000000j | \n", "-0.110502-0.000000j | \n", "... | \n", "0.555041+0.000000j | \n", "0.556708+0.000000j | \n", "0.557821-0.000000j | \n", "0.558406+0.000000j | \n", "0.558483+0.000000j | \n", "0.558074+0.000000j | \n", "0.557198-0.000000j | \n", "0.555870+0.000000j | \n", "0.554108+0.000000j | \n", "0.551925+0.000000j | \n", "|||
| y | \n", "0 | \n", "SG | \n", "PU | \n", "-0.059474-0.000000j | \n", "0.271217+0.000000j | \n", "0.432955+0.000000j | \n", "0.521218-0.000000j | \n", "0.562256-0.000000j | \n", "0.570921-0.000000j | \n", "0.557098+0.000000j | \n", "0.527855-0.000000j | \n", "0.488402-0.000000j | \n", "0.442583-0.000000j | \n", "... | \n", "-0.522724+0.000000j | \n", "-0.532915+0.000000j | \n", "-0.542405-0.000000j | \n", "-0.551224+0.000000j | \n", "-0.559398+0.000000j | \n", "-0.566951-0.000000j | \n", "-0.573903-0.000000j | \n", "-0.580274-0.000000j | \n", "-0.586083+0.000000j | \n", "-0.591343+0.000000j | \n", "||
| -2 | \n", "SG | \n", "PU | \n", "-0.080503+0.000000j | \n", "0.153387-0.000000j | \n", "0.252803-0.000000j | \n", "0.294656-0.000000j | \n", "0.300540-0.000000j | \n", "0.282866-0.000000j | \n", "0.249932-0.000000j | \n", "0.207619-0.000000j | \n", "0.160148-0.000000j | \n", "0.110502-0.000000j | \n", "... | \n", "-0.555041+0.000000j | \n", "-0.556708+0.000000j | \n", "-0.557821+0.000000j | \n", "-0.558406+0.000000j | \n", "-0.558483+0.000000j | \n", "-0.558074+0.000000j | \n", "-0.557198+0.000000j | \n", "-0.555870+0.000000j | \n", "-0.554108+0.000000j | \n", "-0.551925+0.000000j | \n", "|||
| 2 | \n", "SG | \n", "PU | \n", "-0.080503+0.000000j | \n", "0.153387+0.000000j | \n", "0.252803+0.000000j | \n", "0.294656+0.000000j | \n", "0.300540+0.000000j | \n", "0.282866+0.000000j | \n", "0.249932+0.000000j | \n", "0.207619+0.000000j | \n", "0.160148+0.000000j | \n", "0.110502+0.000000j | \n", "... | \n", "-0.555041-0.000000j | \n", "-0.556708-0.000000j | \n", "-0.557821-0.000000j | \n", "-0.558406-0.000000j | \n", "-0.558483-0.000000j | \n", "-0.558074-0.000000j | \n", "-0.557198-0.000000j | \n", "-0.555870-0.000000j | \n", "-0.554108-0.000000j | \n", "-0.551925-0.000000j | \n", "|||
| 6 | \n", "x | \n", "0 | \n", "SG | \n", "PU | \n", "-0.058944+0.000000j | \n", "-0.107815-0.000000j | \n", "-0.158159+0.000000j | \n", "-0.207754-0.000000j | \n", "-0.255279-0.000000j | \n", "-0.299612+0.000000j | \n", "-0.339916-0.000000j | \n", "-0.375688-0.000000j | \n", "-0.406740-0.000000j | \n", "-0.433136-0.000000j | \n", "... | \n", "-0.334833+0.000000j | \n", "-0.323955+0.000000j | \n", "-0.312985+0.000000j | \n", "-0.301929+0.000000j | \n", "-0.290790+0.000000j | \n", "-0.279573+0.000000j | \n", "-0.268281+0.000000j | \n", "-0.256919+0.000000j | \n", "-0.245491-0.000000j | \n", "-0.234000+0.000000j | \n", "|
| -2 | \n", "SG | \n", "PU | \n", "0.040201-0.000000j | \n", "0.073410+0.000000j | \n", "0.107661+0.000000j | \n", "0.141347-0.000000j | \n", "0.173516-0.000000j | \n", "0.203384-0.000000j | \n", "0.230377-0.000000j | \n", "0.254147+0.000000j | \n", "0.274568+0.000000j | \n", "0.291696-0.000000j | \n", "... | \n", "0.201422+0.000000j | \n", "0.193886+0.000000j | \n", "0.186317-0.000000j | \n", "0.178717-0.000000j | \n", "0.171088+0.000000j | \n", "0.163434+0.000000j | \n", "0.155756+0.000000j | \n", "0.148057+0.000000j | \n", "0.140340-0.000000j | \n", "0.132606+0.000000j | \n", "|||
| 2 | \n", "SG | \n", "PU | \n", "0.040201-0.000000j | \n", "0.073410+0.000000j | \n", "0.107661+0.000000j | \n", "0.141347-0.000000j | \n", "0.173516-0.000000j | \n", "0.203384-0.000000j | \n", "0.230377-0.000000j | \n", "0.254147+0.000000j | \n", "0.274568+0.000000j | \n", "0.291696-0.000000j | \n", "... | \n", "0.201422+0.000000j | \n", "0.193886+0.000000j | \n", "0.186317-0.000000j | \n", "0.178717+0.000000j | \n", "0.171088+0.000000j | \n", "0.163434+0.000000j | \n", "0.155756+0.000000j | \n", "0.148057+0.000000j | \n", "0.140340-0.000000j | \n", "0.132606+0.000000j | \n", "|||
| y | \n", "0 | \n", "SG | \n", "PU | \n", "-0.058944+0.000000j | \n", "-0.107815-0.000000j | \n", "-0.158159-0.000000j | \n", "-0.207754+0.000000j | \n", "-0.255279-0.000000j | \n", "-0.299612+0.000000j | \n", "-0.339916+0.000000j | \n", "-0.375688-0.000000j | \n", "-0.406740-0.000000j | \n", "-0.433136-0.000000j | \n", "... | \n", "-0.334833+0.000000j | \n", "-0.323955+0.000000j | \n", "-0.312985+0.000000j | \n", "-0.301929+0.000000j | \n", "-0.290790+0.000000j | \n", "-0.279573-0.000000j | \n", "-0.268281-0.000000j | \n", "-0.256919+0.000000j | \n", "-0.245491+0.000000j | \n", "-0.234000+0.000000j | \n", "||
| -2 | \n", "SG | \n", "PU | \n", "-0.040201+0.000000j | \n", "-0.073410+0.000000j | \n", "-0.107661+0.000000j | \n", "-0.141347+0.000000j | \n", "-0.173516+0.000000j | \n", "-0.203384+0.000000j | \n", "-0.230377-0.000000j | \n", "-0.254147+0.000000j | \n", "-0.274568+0.000000j | \n", "-0.291696+0.000000j | \n", "... | \n", "-0.201422+0.000000j | \n", "-0.193886+0.000000j | \n", "-0.186317+0.000000j | \n", "-0.178717+0.000000j | \n", "-0.171088+0.000000j | \n", "-0.163434+0.000000j | \n", "-0.155756+0.000000j | \n", "-0.148057+0.000000j | \n", "-0.140340+0.000000j | \n", "-0.132606+0.000000j | \n", "|||
| 2 | \n", "SG | \n", "PU | \n", "-0.040201-0.000000j | \n", "-0.073410-0.000000j | \n", "-0.107661-0.000000j | \n", "-0.141347-0.000000j | \n", "-0.173516-0.000000j | \n", "-0.203384-0.000000j | \n", "-0.230377-0.000000j | \n", "-0.254147-0.000000j | \n", "-0.274568-0.000000j | \n", "-0.291696-0.000000j | \n", "... | \n", "-0.201422-0.000000j | \n", "-0.193886-0.000000j | \n", "-0.186317-0.000000j | \n", "-0.178717-0.000000j | \n", "-0.171088-0.000000j | \n", "-0.163434-0.000000j | \n", "-0.155756-0.000000j | \n", "-0.148057-0.000000j | \n", "-0.140340-0.000000j | \n", "-0.132606-0.000000j | \n", "|||
| 8 | \n", "x | \n", "0 | \n", "SG | \n", "PU | \n", "0.000181-0.000000j | \n", "0.000676+0.000000j | \n", "0.001048+0.000000j | \n", "0.001561-0.000000j | \n", "0.002372-0.000000j | \n", "0.003530-0.000000j | \n", "0.005048-0.000000j | \n", "0.006928+0.000000j | \n", "0.009163+0.000000j | \n", "0.011727-0.000000j | \n", "... | \n", "0.084583+0.000000j | \n", "0.085252-0.000000j | \n", "0.085848-0.000000j | \n", "0.086372-0.000000j | \n", "0.086827+0.000000j | \n", "0.087214+0.000000j | \n", "0.087535+0.000000j | \n", "0.087790+0.000000j | \n", "0.087983+0.000000j | \n", "0.088113+0.000000j | \n", "|
| -2 | \n", "SG | \n", "PU | \n", "-0.000115-0.000000j | \n", "-0.000427-0.000000j | \n", "-0.000665+0.000000j | \n", "-0.000996-0.000000j | \n", "-0.001512-0.000000j | \n", "-0.002244-0.000000j | \n", "-0.003199-0.000000j | \n", "-0.004381-0.000000j | \n", "-0.005784-0.000000j | \n", "-0.007393-0.000000j | \n", "... | \n", "-0.051392-0.000000j | \n", "-0.051726-0.000000j | \n", "-0.052010+0.000000j | \n", "-0.052248+0.000000j | \n", "-0.052440+0.000000j | \n", "-0.052587+0.000000j | \n", "-0.052690+0.000000j | \n", "-0.052750-0.000000j | \n", "-0.052766+0.000000j | \n", "-0.052741-0.000000j | \n", "|||
| 2 | \n", "SG | \n", "PU | \n", "-0.000115-0.000000j | \n", "-0.000427-0.000000j | \n", "-0.000665+0.000000j | \n", "-0.000996-0.000000j | \n", "-0.001512-0.000000j | \n", "-0.002244-0.000000j | \n", "-0.003199-0.000000j | \n", "-0.004381-0.000000j | \n", "-0.005784-0.000000j | \n", "-0.007393-0.000000j | \n", "... | \n", "-0.051392-0.000000j | \n", "-0.051726-0.000000j | \n", "-0.052010+0.000000j | \n", "-0.052248+0.000000j | \n", "-0.052440+0.000000j | \n", "-0.052587+0.000000j | \n", "-0.052690+0.000000j | \n", "-0.052750-0.000000j | \n", "-0.052766+0.000000j | \n", "-0.052741-0.000000j | \n", "|||
| y | \n", "0 | \n", "SG | \n", "PU | \n", "0.000181-0.000000j | \n", "0.000676+0.000000j | \n", "0.001048+0.000000j | \n", "0.001561-0.000000j | \n", "0.002372-0.000000j | \n", "0.003530-0.000000j | \n", "0.005048-0.000000j | \n", "0.006928-0.000000j | \n", "0.009163-0.000000j | \n", "0.011727-0.000000j | \n", "... | \n", "0.084583+0.000000j | \n", "0.085252+0.000000j | \n", "0.085848+0.000000j | \n", "0.086372+0.000000j | \n", "0.086827+0.000000j | \n", "0.087214+0.000000j | \n", "0.087535+0.000000j | \n", "0.087790+0.000000j | \n", "0.087983-0.000000j | \n", "0.088113+0.000000j | \n", "||
| -2 | \n", "SG | \n", "PU | \n", "0.000115-0.000000j | \n", "0.000427-0.000000j | \n", "0.000665-0.000000j | \n", "0.000996-0.000000j | \n", "0.001512-0.000000j | \n", "0.002244-0.000000j | \n", "0.003199-0.000000j | \n", "0.004381-0.000000j | \n", "0.005784-0.000000j | \n", "0.007393-0.000000j | \n", "... | \n", "0.051392-0.000000j | \n", "0.051726-0.000000j | \n", "0.052010-0.000000j | \n", "0.052248-0.000000j | \n", "0.052440-0.000000j | \n", "0.052587-0.000000j | \n", "0.052690+0.000000j | \n", "0.052750-0.000000j | \n", "0.052766-0.000000j | \n", "0.052741-0.000000j | \n", "|||
| 2 | \n", "SG | \n", "PU | \n", "0.000115-0.000000j | \n", "0.000427+0.000000j | \n", "0.000665-0.000000j | \n", "0.000996+0.000000j | \n", "0.001512+0.000000j | \n", "0.002244+0.000000j | \n", "0.003199+0.000000j | \n", "0.004381-0.000000j | \n", "0.005784+0.000000j | \n", "0.007393+0.000000j | \n", "... | \n", "0.051392+0.000000j | \n", "0.051726+0.000000j | \n", "0.052010+0.000000j | \n", "0.052248+0.000000j | \n", "0.052440+0.000000j | \n", "0.052587+0.000000j | \n", "0.052690+0.000000j | \n", "0.052750+0.000000j | \n", "0.052766+0.000000j | \n", "0.052741+0.000000j | \n", "|||
| 10 | \n", "x | \n", "0 | \n", "SG | \n", "PU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "-0.000134-0.000000j | \n", "... | \n", "-0.008993-0.000000j | \n", "-0.009385+0.000000j | \n", "-0.009786+0.000000j | \n", "-0.010196+0.000000j | \n", "-0.010616+0.000000j | \n", "-0.011047+0.000000j | \n", "-0.011490-0.000000j | \n", "-0.011946+0.000000j | \n", "-0.012415-0.000000j | \n", "-0.012898-0.000000j | \n", "|
| -2 | \n", "SG | \n", "PU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "... | \n", "0.005321+0.000000j | \n", "0.005549-0.000000j | \n", "0.005782-0.000000j | \n", "0.006019-0.000000j | \n", "0.006262+0.000000j | \n", "0.006512+0.000000j | \n", "0.006767+0.000000j | \n", "0.007030+0.000000j | \n", "0.007299+0.000000j | \n", "0.007577+0.000000j | \n", "|||
| 2 | \n", "SG | \n", "PU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "... | \n", "0.005321+0.000000j | \n", "0.005549-0.000000j | \n", "0.005782-0.000000j | \n", "0.006019-0.000000j | \n", "0.006262+0.000000j | \n", "0.006512+0.000000j | \n", "0.006767+0.000000j | \n", "0.007030+0.000000j | \n", "0.007299+0.000000j | \n", "0.007577+0.000000j | \n", "|||
| y | \n", "0 | \n", "SG | \n", "PU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "-0.000134-0.000000j | \n", "... | \n", "-0.008993+0.000000j | \n", "-0.009385+0.000000j | \n", "-0.009786-0.000000j | \n", "-0.010196+0.000000j | \n", "-0.010616+0.000000j | \n", "-0.011047-0.000000j | \n", "-0.011490+0.000000j | \n", "-0.011946+0.000000j | \n", "-0.012415+0.000000j | \n", "-0.012898+0.000000j | \n", "||
| -2 | \n", "SG | \n", "PU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "... | \n", "-0.005321+0.000000j | \n", "-0.005549+0.000000j | \n", "-0.005782+0.000000j | \n", "-0.006019+0.000000j | \n", "-0.006262+0.000000j | \n", "-0.006512+0.000000j | \n", "-0.006767+0.000000j | \n", "-0.007030+0.000000j | \n", "-0.007299+0.000000j | \n", "-0.007577+0.000000j | \n", "|||
| 2 | \n", "SG | \n", "PU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "... | \n", "-0.005321-0.000000j | \n", "-0.005549-0.000000j | \n", "-0.005782-0.000000j | \n", "-0.006019-0.000000j | \n", "-0.006262-0.000000j | \n", "-0.006512-0.000000j | \n", "-0.006767-0.000000j | \n", "-0.007030-0.000000j | \n", "-0.007299-0.000000j | \n", "-0.007577-0.000000j | \n", "|||
| 12 | \n", "x | \n", "0 | \n", "SG | \n", "PU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "... | \n", "0.000625+0.000000j | \n", "0.000674-0.000000j | \n", "0.000726-0.000000j | \n", "0.000781-0.000000j | \n", "0.000839+0.000000j | \n", "0.000901-0.000000j | \n", "0.000967+0.000000j | \n", "0.001037+0.000000j | \n", "0.001111+0.000000j | \n", "0.001190+0.000000j | \n", "|
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| 2 | \n", "SG | \n", "PU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "... | \n", "-0.000362+0.000000j | \n", "-0.000390+0.000000j | \n", "-0.000419+0.000000j | \n", "-0.000451+0.000000j | \n", "-0.000484+0.000000j | \n", "-0.000520+0.000000j | \n", "-0.000558-0.000000j | \n", "-0.000598-0.000000j | \n", "-0.000640-0.000000j | \n", "-0.000686-0.000000j | \n", "|||
| y | \n", "0 | \n", "SG | \n", "PU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "... | \n", "0.000625+0.000000j | \n", "0.000674+0.000000j | \n", "0.000726+0.000000j | \n", "0.000781-0.000000j | \n", "0.000839+0.000000j | \n", "0.000901+0.000000j | \n", "0.000967+0.000000j | \n", "0.001037+0.000000j | \n", "0.001111-0.000000j | \n", "0.001190+0.000000j | \n", "||
| -2 | \n", "SG | \n", "PU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "... | \n", "0.000362-0.000000j | \n", "0.000390-0.000000j | \n", "0.000419-0.000000j | \n", "0.000451-0.000000j | \n", "0.000484-0.000000j | \n", "0.000520+0.000000j | \n", "0.000558-0.000000j | \n", "0.000598-0.000000j | \n", "0.000640-0.000000j | \n", "0.000686-0.000000j | \n", "|||
| 2 | \n", "SG | \n", "PU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "... | \n", "0.000362+0.000000j | \n", "0.000390+0.000000j | \n", "0.000419+0.000000j | \n", "0.000451+0.000000j | \n", "0.000484+0.000000j | \n", "0.000520+0.000000j | \n", "0.000558+0.000000j | \n", "0.000598+0.000000j | \n", "0.000640+0.000000j | \n", "0.000686+0.000000j | \n", "|||
| SU | \n", "0 | \n", "z | \n", "0 | \n", "SG | \n", "SU | \n", "1.000000-0.000000j | \n", "1.000000-0.000000j | \n", "1.000000-0.000000j | \n", "1.000000-0.000000j | \n", "1.000000-0.000000j | \n", "1.000000-0.000000j | \n", "1.000000-0.000000j | \n", "1.000000-0.000000j | \n", "1.000000-0.000000j | \n", "1.000000-0.000000j | \n", "... | \n", "1.000000+0.000000j | \n", "1.000000+0.000000j | \n", "1.000000+0.000000j | \n", "1.000000+0.000000j | \n", "1.000000+0.000000j | \n", "1.000000+0.000000j | \n", "1.000000+0.000000j | \n", "1.000000+0.000000j | \n", "1.000000+0.000000j | \n", "1.000000+0.000000j | \n", "
| 2 | \n", "z | \n", "0 | \n", "SG | \n", "SU | \n", "0.784764-0.000000j | \n", "0.292636+0.000000j | \n", "0.110286-0.000000j | \n", "0.047655+0.000000j | \n", "0.053351-0.000000j | \n", "0.100478-0.000000j | \n", "0.172894-0.000000j | \n", "0.260212-0.000000j | \n", "0.355478-0.000000j | \n", "0.453965-0.000000j | \n", "... | \n", "0.307136+0.000000j | \n", "0.353015-0.000000j | \n", "0.404836+0.000000j | \n", "0.459405-0.000000j | \n", "0.514462-0.000000j | \n", "0.568485+0.000000j | \n", "0.620505+0.000000j | \n", "0.669947-0.000000j | \n", "0.716512-0.000000j | \n", "0.760083+0.000000j | \n", "|
| 4 | \n", "z | \n", "0 | \n", "SG | \n", "SU | \n", "-0.040643+0.000000j | \n", "-0.472493-0.000000j | \n", "-0.596717-0.000000j | \n", "-0.603036-0.000000j | \n", "-0.543465+0.000000j | \n", "-0.445631+0.000000j | \n", "-0.326262-0.000000j | \n", "-0.196158-0.000000j | \n", "-0.062516+0.000000j | \n", "0.069865-0.000000j | \n", "... | \n", "-0.569503-0.000000j | \n", "-0.517657+0.000000j | \n", "-0.458173-0.000000j | \n", "-0.395217-0.000000j | \n", "-0.331713-0.000000j | \n", "-0.269614-0.000000j | \n", "-0.210149-0.000000j | \n", "-0.154034-0.000000j | \n", "-0.101629-0.000000j | \n", "-0.053060+0.000000j | \n", "|
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| 12 | \n", "z | \n", "0 | \n", "SG | \n", "SU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "... | \n", "-0.006051-0.000000j | \n", "-0.006437+0.000000j | \n", "-0.006788-0.000000j | \n", "-0.007113+0.000000j | \n", "-0.007416+0.000000j | \n", "-0.007706-0.000000j | \n", "-0.007985+0.000000j | \n", "-0.008259+0.000000j | \n", "-0.008530+0.000000j | \n", "-0.008801-0.000000j | \n", "|
| 14 | \n", "z | \n", "0 | \n", "SG | \n", "SU | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "... | \n", "0.000422+0.000000j | \n", "0.000449+0.000000j | \n", "0.000476+0.000000j | \n", "0.000501+0.000000j | \n", "0.000525+0.000000j | \n", "0.000549+0.000000j | \n", "0.000573+0.000000j | \n", "0.000598+0.000000j | \n", "0.000622+0.000000j | \n", "0.000648+0.000000j | \n", "
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| -2 | \n", "-0.512102+0.000000j | \n", "-0.586763+0.000000j | \n", "-0.614632+0.000000j | \n", "-0.622681+0.000000j | \n", "-0.618586+0.000000j | \n", "-0.606800+0.000000j | \n", "-0.590309+0.000000j | \n", "-0.571219+0.000000j | \n", "-0.551014+0.000000j | \n", "-0.530717+0.000000j | \n", "... | \n", "-0.322705+0.000000j | \n", "-0.323603+0.000000j | \n", "-0.324693+0.000000j | \n", "-0.325966+0.000000j | \n", "-0.327414+0.000000j | \n", "-0.329029+0.000000j | \n", "-0.330804+0.000000j | \n", "-0.332734+0.000000j | \n", "-0.334812+0.000000j | \n", "-0.337033+0.000000j | \n", "||
| 2 | \n", "-0.512102-0.000000j | \n", "-0.586763-0.000000j | \n", "-0.614632-0.000000j | \n", "-0.622681-0.000000j | \n", "-0.618586-0.000000j | \n", "-0.606800-0.000000j | \n", "-0.590309-0.000000j | \n", "-0.571219-0.000000j | \n", "-0.551014-0.000000j | \n", "-0.530717-0.000000j | \n", "... | \n", "-0.322705-0.000000j | \n", "-0.323603-0.000000j | \n", "-0.324693-0.000000j | \n", "-0.325966-0.000000j | \n", "-0.327414-0.000000j | \n", "-0.329029-0.000000j | \n", "-0.330804-0.000000j | \n", "-0.332734-0.000000j | \n", "-0.334812-0.000000j | \n", "-0.337033-0.000000j | \n", "||
| 4 | \n", "z | \n", "0 | \n", "-0.040643+0.000000j | \n", "-0.472493-0.000000j | \n", "-0.596717-0.000000j | \n", "-0.603036-0.000000j | \n", "-0.543465+0.000000j | \n", "-0.445631+0.000000j | \n", "-0.326262-0.000000j | \n", "-0.196158-0.000000j | \n", "-0.062516+0.000000j | \n", "0.069865-0.000000j | \n", "... | \n", "-0.569503-0.000000j | \n", "-0.517657+0.000000j | \n", "-0.458173-0.000000j | \n", "-0.395217-0.000000j | \n", "-0.331713-0.000000j | \n", "-0.269614-0.000000j | \n", "-0.210149-0.000000j | \n", "-0.154034-0.000000j | \n", "-0.101629-0.000000j | \n", "-0.053060+0.000000j | \n", "
| x | \n", "0 | \n", "-0.059474-0.000000j | \n", "0.271217+0.000000j | \n", "0.432955-0.000000j | \n", "0.521218-0.000000j | \n", "0.562256-0.000000j | \n", "0.570921-0.000000j | \n", "0.557098-0.000000j | \n", "0.527855+0.000000j | \n", "0.488402+0.000000j | \n", "0.442583-0.000000j | \n", "... | \n", "-0.522724+0.000000j | \n", "-0.532915+0.000000j | \n", "-0.542405+0.000000j | \n", "-0.551224+0.000000j | \n", "-0.559398+0.000000j | \n", "-0.566951-0.000000j | \n", "-0.573903-0.000000j | \n", "-0.580274-0.000000j | \n", "-0.586083+0.000000j | \n", "-0.591343+0.000000j | \n", "|
| -2 | \n", "0.080503-0.000000j | \n", "-0.153387-0.000000j | \n", "-0.252803-0.000000j | \n", "-0.294656-0.000000j | \n", "-0.300540-0.000000j | \n", "-0.282866+0.000000j | \n", "-0.249932-0.000000j | \n", "-0.207619-0.000000j | \n", "-0.160148-0.000000j | \n", "-0.110502-0.000000j | \n", "... | \n", "0.555041+0.000000j | \n", "0.556708+0.000000j | \n", "0.557821-0.000000j | \n", "0.558406+0.000000j | \n", "0.558483+0.000000j | \n", "0.558074+0.000000j | \n", "0.557198-0.000000j | \n", "0.555870+0.000000j | \n", "0.554108+0.000000j | \n", "0.551925+0.000000j | \n", "||
| 2 | \n", "0.080503-0.000000j | \n", "-0.153387-0.000000j | \n", "-0.252803-0.000000j | \n", "-0.294656-0.000000j | \n", "-0.300540-0.000000j | \n", "-0.282866+0.000000j | \n", "-0.249932-0.000000j | \n", "-0.207619-0.000000j | \n", "-0.160148-0.000000j | \n", "-0.110502-0.000000j | \n", "... | \n", "0.555041+0.000000j | \n", "0.556708+0.000000j | \n", "0.557821-0.000000j | \n", "0.558406+0.000000j | \n", "0.558483+0.000000j | \n", "0.558074+0.000000j | \n", "0.557198-0.000000j | \n", "0.555870+0.000000j | \n", "0.554108+0.000000j | \n", "0.551925+0.000000j | \n", "||
| y | \n", "0 | \n", "-0.059474-0.000000j | \n", "0.271217+0.000000j | \n", "0.432955+0.000000j | \n", "0.521218-0.000000j | \n", "0.562256-0.000000j | \n", "0.570921-0.000000j | \n", "0.557098+0.000000j | \n", "0.527855-0.000000j | \n", "0.488402-0.000000j | \n", "0.442583-0.000000j | \n", "... | \n", "-0.522724+0.000000j | \n", "-0.532915+0.000000j | \n", "-0.542405-0.000000j | \n", "-0.551224+0.000000j | \n", "-0.559398+0.000000j | \n", "-0.566951-0.000000j | \n", "-0.573903-0.000000j | \n", "-0.580274-0.000000j | \n", "-0.586083+0.000000j | \n", "-0.591343+0.000000j | \n", "|
| -2 | \n", "-0.080503+0.000000j | \n", "0.153387-0.000000j | \n", "0.252803-0.000000j | \n", "0.294656-0.000000j | \n", "0.300540-0.000000j | \n", "0.282866-0.000000j | \n", "0.249932-0.000000j | \n", "0.207619-0.000000j | \n", "0.160148-0.000000j | \n", "0.110502-0.000000j | \n", "... | \n", "-0.555041+0.000000j | \n", "-0.556708+0.000000j | \n", "-0.557821+0.000000j | \n", "-0.558406+0.000000j | \n", "-0.558483+0.000000j | \n", "-0.558074+0.000000j | \n", "-0.557198+0.000000j | \n", "-0.555870+0.000000j | \n", "-0.554108+0.000000j | \n", "-0.551925+0.000000j | \n", "||
| 2 | \n", "-0.080503+0.000000j | \n", "0.153387+0.000000j | \n", "0.252803+0.000000j | \n", "0.294656+0.000000j | \n", "0.300540+0.000000j | \n", "0.282866+0.000000j | \n", "0.249932+0.000000j | \n", "0.207619+0.000000j | \n", "0.160148+0.000000j | \n", "0.110502+0.000000j | \n", "... | \n", "-0.555041-0.000000j | \n", "-0.556708-0.000000j | \n", "-0.557821-0.000000j | \n", "-0.558406-0.000000j | \n", "-0.558483-0.000000j | \n", "-0.558074-0.000000j | \n", "-0.557198-0.000000j | \n", "-0.555870-0.000000j | \n", "-0.554108-0.000000j | \n", "-0.551925-0.000000j | \n", "||
| 6 | \n", "z | \n", "0 | \n", "0.067996+0.000000j | \n", "0.124559+0.000000j | \n", "0.181056-0.000000j | \n", "0.236287+0.000000j | \n", "0.289141-0.000000j | \n", "0.338700-0.000000j | \n", "0.384294-0.000000j | \n", "0.425467-0.000000j | \n", "0.461963-0.000000j | \n", "0.493736-0.000000j | \n", "... | \n", "-0.012438-0.000000j | \n", "-0.026005+0.000000j | \n", "-0.036082-0.000000j | \n", "-0.043618+0.000000j | \n", "-0.049363-0.000000j | \n", "-0.053889+0.000000j | \n", "-0.057618-0.000000j | \n", "-0.060854-0.000000j | \n", "-0.063810-0.000000j | \n", "-0.066634+0.000000j | \n", "
| x | \n", "0 | \n", "-0.058944+0.000000j | \n", "-0.107815-0.000000j | \n", "-0.158159+0.000000j | \n", "-0.207754-0.000000j | \n", "-0.255279-0.000000j | \n", "-0.299612+0.000000j | \n", "-0.339916-0.000000j | \n", "-0.375688-0.000000j | \n", "-0.406740-0.000000j | \n", "-0.433136-0.000000j | \n", "... | \n", "-0.334833+0.000000j | \n", "-0.323955+0.000000j | \n", "-0.312985+0.000000j | \n", "-0.301929+0.000000j | \n", "-0.290790+0.000000j | \n", "-0.279573+0.000000j | \n", "-0.268281+0.000000j | \n", "-0.256919+0.000000j | \n", "-0.245491-0.000000j | \n", "-0.234000+0.000000j | \n", "|
| -2 | \n", "0.040201-0.000000j | \n", "0.073410+0.000000j | \n", "0.107661+0.000000j | \n", "0.141347-0.000000j | \n", "0.173516-0.000000j | \n", "0.203384-0.000000j | \n", "0.230377-0.000000j | \n", "0.254147+0.000000j | \n", "0.274568+0.000000j | \n", "0.291696-0.000000j | \n", "... | \n", "0.201422+0.000000j | \n", "0.193886+0.000000j | \n", "0.186317-0.000000j | \n", "0.178717-0.000000j | \n", "0.171088+0.000000j | \n", "0.163434+0.000000j | \n", "0.155756+0.000000j | \n", "0.148057+0.000000j | \n", "0.140340-0.000000j | \n", "0.132606+0.000000j | \n", "||
| 2 | \n", "0.040201-0.000000j | \n", "0.073410+0.000000j | \n", "0.107661+0.000000j | \n", "0.141347-0.000000j | \n", "0.173516-0.000000j | \n", "0.203384-0.000000j | \n", "0.230377-0.000000j | \n", "0.254147+0.000000j | \n", "0.274568+0.000000j | \n", "0.291696-0.000000j | \n", "... | \n", "0.201422+0.000000j | \n", "0.193886+0.000000j | \n", "0.186317-0.000000j | \n", "0.178717+0.000000j | \n", "0.171088+0.000000j | \n", "0.163434+0.000000j | \n", "0.155756+0.000000j | \n", "0.148057+0.000000j | \n", "0.140340-0.000000j | \n", "0.132606+0.000000j | \n", "||
| y | \n", "0 | \n", "-0.058944+0.000000j | \n", "-0.107815-0.000000j | \n", "-0.158159-0.000000j | \n", "-0.207754+0.000000j | \n", "-0.255279-0.000000j | \n", "-0.299612+0.000000j | \n", "-0.339916+0.000000j | \n", "-0.375688-0.000000j | \n", "-0.406740-0.000000j | \n", "-0.433136-0.000000j | \n", "... | \n", "-0.334833+0.000000j | \n", "-0.323955+0.000000j | \n", "-0.312985+0.000000j | \n", "-0.301929+0.000000j | \n", "-0.290790+0.000000j | \n", "-0.279573-0.000000j | \n", "-0.268281-0.000000j | \n", "-0.256919+0.000000j | \n", "-0.245491+0.000000j | \n", "-0.234000+0.000000j | \n", "|
| -2 | \n", "-0.040201+0.000000j | \n", "-0.073410+0.000000j | \n", "-0.107661+0.000000j | \n", "-0.141347+0.000000j | \n", "-0.173516+0.000000j | \n", "-0.203384+0.000000j | \n", "-0.230377-0.000000j | \n", "-0.254147+0.000000j | \n", "-0.274568+0.000000j | \n", "-0.291696+0.000000j | \n", "... | \n", "-0.201422+0.000000j | \n", "-0.193886+0.000000j | \n", "-0.186317+0.000000j | \n", "-0.178717+0.000000j | \n", "-0.171088+0.000000j | \n", "-0.163434+0.000000j | \n", "-0.155756+0.000000j | \n", "-0.148057+0.000000j | \n", "-0.140340+0.000000j | \n", "-0.132606+0.000000j | \n", "||
| 2 | \n", "-0.040201-0.000000j | \n", "-0.073410-0.000000j | \n", "-0.107661-0.000000j | \n", "-0.141347-0.000000j | \n", "-0.173516-0.000000j | \n", "-0.203384-0.000000j | \n", "-0.230377-0.000000j | \n", "-0.254147-0.000000j | \n", "-0.274568-0.000000j | \n", "-0.291696-0.000000j | \n", "... | \n", "-0.201422-0.000000j | \n", "-0.193886-0.000000j | \n", "-0.186317-0.000000j | \n", "-0.178717-0.000000j | \n", "-0.171088-0.000000j | \n", "-0.163434-0.000000j | \n", "-0.155756-0.000000j | \n", "-0.148057-0.000000j | \n", "-0.140340-0.000000j | \n", "-0.132606-0.000000j | \n", "||
| 8 | \n", "z | \n", "0 | \n", "-0.000240-0.000000j | \n", "-0.000812-0.000000j | \n", "-0.001227-0.000000j | \n", "-0.001840-0.000000j | \n", "-0.002813+0.000000j | \n", "-0.004167-0.000000j | \n", "-0.005886+0.000000j | \n", "-0.007949-0.000000j | \n", "-0.010322-0.000000j | \n", "-0.012952-0.000000j | \n", "... | \n", "0.016562-0.000000j | \n", "0.000498+0.000000j | \n", "-0.014200+0.000000j | \n", "-0.027442-0.000000j | \n", "-0.039244+0.000000j | \n", "-0.049687+0.000000j | \n", "-0.058880+0.000000j | \n", "-0.066945-0.000000j | \n", "-0.074001+0.000000j | \n", "-0.080160-0.000000j | \n", "
| x | \n", "0 | \n", "0.000181-0.000000j | \n", "0.000676+0.000000j | \n", "0.001048+0.000000j | \n", "0.001561-0.000000j | \n", "0.002372-0.000000j | \n", "0.003530-0.000000j | \n", "0.005048-0.000000j | \n", "0.006928+0.000000j | \n", "0.009163+0.000000j | \n", "0.011727-0.000000j | \n", "... | \n", "0.084583+0.000000j | \n", "0.085252-0.000000j | \n", "0.085848-0.000000j | \n", "0.086372-0.000000j | \n", "0.086827+0.000000j | \n", "0.087214+0.000000j | \n", "0.087535+0.000000j | \n", "0.087790+0.000000j | \n", "0.087983+0.000000j | \n", "0.088113+0.000000j | \n", "|
| -2 | \n", "-0.000115-0.000000j | \n", "-0.000427-0.000000j | \n", "-0.000665+0.000000j | \n", "-0.000996-0.000000j | \n", "-0.001512-0.000000j | \n", "-0.002244-0.000000j | \n", "-0.003199-0.000000j | \n", "-0.004381-0.000000j | \n", "-0.005784-0.000000j | \n", "-0.007393-0.000000j | \n", "... | \n", "-0.051392-0.000000j | \n", "-0.051726-0.000000j | \n", "-0.052010+0.000000j | \n", "-0.052248+0.000000j | \n", "-0.052440+0.000000j | \n", "-0.052587+0.000000j | \n", "-0.052690+0.000000j | \n", "-0.052750-0.000000j | \n", "-0.052766+0.000000j | \n", "-0.052741-0.000000j | \n", "||
| 2 | \n", "-0.000115-0.000000j | \n", "-0.000427-0.000000j | \n", "-0.000665+0.000000j | \n", "-0.000996-0.000000j | \n", "-0.001512-0.000000j | \n", "-0.002244-0.000000j | \n", "-0.003199-0.000000j | \n", "-0.004381-0.000000j | \n", "-0.005784-0.000000j | \n", "-0.007393-0.000000j | \n", "... | \n", "-0.051392-0.000000j | \n", "-0.051726-0.000000j | \n", "-0.052010+0.000000j | \n", "-0.052248+0.000000j | \n", "-0.052440+0.000000j | \n", "-0.052587+0.000000j | \n", "-0.052690+0.000000j | \n", "-0.052750-0.000000j | \n", "-0.052766+0.000000j | \n", "-0.052741-0.000000j | \n", "||
| y | \n", "0 | \n", "0.000181-0.000000j | \n", "0.000676+0.000000j | \n", "0.001048+0.000000j | \n", "0.001561-0.000000j | \n", "0.002372-0.000000j | \n", "0.003530-0.000000j | \n", "0.005048-0.000000j | \n", "0.006928-0.000000j | \n", "0.009163-0.000000j | \n", "0.011727-0.000000j | \n", "... | \n", "0.084583+0.000000j | \n", "0.085252+0.000000j | \n", "0.085848+0.000000j | \n", "0.086372+0.000000j | \n", "0.086827+0.000000j | \n", "0.087214+0.000000j | \n", "0.087535+0.000000j | \n", "0.087790+0.000000j | \n", "0.087983-0.000000j | \n", "0.088113+0.000000j | \n", "|
| -2 | \n", "0.000115-0.000000j | \n", "0.000427-0.000000j | \n", "0.000665-0.000000j | \n", "0.000996-0.000000j | \n", "0.001512-0.000000j | \n", "0.002244-0.000000j | \n", "0.003199-0.000000j | \n", "0.004381-0.000000j | \n", "0.005784-0.000000j | \n", "0.007393-0.000000j | \n", "... | \n", "0.051392-0.000000j | \n", "0.051726-0.000000j | \n", "0.052010-0.000000j | \n", "0.052248-0.000000j | \n", "0.052440-0.000000j | \n", "0.052587-0.000000j | \n", "0.052690+0.000000j | \n", "0.052750-0.000000j | \n", "0.052766-0.000000j | \n", "0.052741-0.000000j | \n", "||
| 2 | \n", "0.000115-0.000000j | \n", "0.000427+0.000000j | \n", "0.000665-0.000000j | \n", "0.000996+0.000000j | \n", "0.001512+0.000000j | \n", "0.002244+0.000000j | \n", "0.003199+0.000000j | \n", "0.004381-0.000000j | \n", "0.005784+0.000000j | \n", "0.007393+0.000000j | \n", "... | \n", "0.051392+0.000000j | \n", "0.051726+0.000000j | \n", "0.052010+0.000000j | \n", "0.052248+0.000000j | \n", "0.052440+0.000000j | \n", "0.052587+0.000000j | \n", "0.052690+0.000000j | \n", "0.052750+0.000000j | \n", "0.052766+0.000000j | \n", "0.052741+0.000000j | \n", "||
| 10 | \n", "z | \n", "0 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "0.000137-0.000000j | \n", "... | \n", "0.036612+0.000000j | \n", "0.039931+0.000000j | \n", "0.042889+0.000000j | \n", "0.045534-0.000000j | \n", "0.047912+0.000000j | \n", "0.050071+0.000000j | \n", "0.052050+0.000000j | \n", "0.053883+0.000000j | \n", "0.055598+0.000000j | \n", "0.057219+0.000000j | \n", "
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46 rows × 51 columns
\n", "| Software | Version |
|---|---|
| Python | 3.7.3 64bit [MSC v.1915 64 bit (AMD64)] |
| IPython | 7.12.0 |
| OS | Windows 10 10.0.18362 SP0 |
| epsproc | 1.2.5-dev |
| xarray | 0.15.0 |
| Tue Apr 14 15:25:37 2020 Eastern Daylight Time | |